Algorithm efficiency and Big-O notation

• What does algorithm efficiency measure?

  The time based on input size
• What does algorithm efficiency describe?

  How fast an algorithm runs
• How do the different categories of running time complexity compare in terms of efficiency?

  The categories are ordered from most efficient (O(1) - Best) to least efficient (O(n!), O(n^n), O(n^c) - Worst).
• How do efficient algorithms reduce resource usage?

  They minimize energy consumption and memory needed
• What is the x-axis label in the image?

  Input Size n
• Why is algorithm efficiency important?

  It saves time, reduces resource usage, and improves scalability
• Why is understanding Big O notation important?

  • Helps choose efficient algorithms
  • Allows comparison of algorithm performance
  • Aids in predicting runtime based on input size
• How does the running time complexity of an algorithm with O(n) scale as the input size increases, compared to an algorithm with O(logn)?

  O(n) scales linearly with input size, while O(logn) scales logarithmically, making O(logn) more efficient for large inputs
• Which Big O time complexity is the slowest?

  $O(2^{n})$
• What is the Big-O notation for Binary Search?

  $O(\log n)$
• What does $O(n^{2})$ represent in Big O notation?


  Quadratic time
• What is the growth rate of $O(1)$?


  Constant
• Which Big O time complexity is the fastest?

  $O(1)$
• What are the key reasons for algorithm efficiency's importance?

  • Saves time
  • Reduces resource usage
  • Enables scalability
  • Improves user experience
• What does $O(n)$ signify in Big O notation?


  Linear time
• Why is Binary Search faster for large datasets?

  It eliminates half the numbers each time
• How does the time taken grow as input size increases?

  At different rates along the curves
• How does Big O notation help in algorithm comparison?

  It simplifies comparing different algorithms' efficiency
• What is the second search algorithm mentioned?

  Binary Search
• What does $O(1)$ represent in Big O notation?


  Constant time
• What does $O(n)$ signify in Linear Search?


  Time increases proportionally with input size
• What are the growth rates of the worst time complexities?

  Quadratic and Exponential
• How does Binary Search find the target?

  It divides the sorted list in half repeatedly
• Why is algorithm efficiency beneficial for mobile devices?

  It minimizes energy consumption and memory usage
• Compare the efficiency of Linear Search and Binary Search.

  • Linear Search:
  • Checks each element sequentially
  • Big-O notation: $O(n)$
  • Example: 1000 steps for 1000 numbers

  
  

  • Binary Search:
  • Divides the list in half repeatedly
  • Big-O notation: $O(\log n)$
  • Example: 10 steps for 1000 numbers
• How do efficient algorithms save time?

  They complete tasks faster with larger datasets
• What characterizes an inefficient algorithm?

  Takes longer, especially with larger inputs
• What is the growth rate of $O(n)$?


  Linear
• How does Linear Search operate?

  It checks each element one by one
• What is the Big-O notation for Linear Search?

  $O(n)$
• What is the growth rate of $O(n \log n)$?


  Linearithmic
• How does algorithm efficiency enable scalability?

  It allows systems to handle massive traffic without slowdowns
• What is the time complexity of linear search?

  $O(n)$
• What are the different categories of running time complexity shown in the image?

  • O(1) - Best
  • O(logn) - Good
  • O(n) - Fair
  • O(nlogn) - Bad
  • O(n!), O(n^n), O(n^c) - Worst
• What is Big O notation used for?

  To measure algorithm runtime changes
• What is the y-axis label in the image?

  Running Time Complexity in terms of Big-O O(f(n))
• What is the growth rate of $O(\log n)$?


  Logarithmic
• What is the first search algorithm mentioned?

  Linear Search
• What is the time complexity of binary search?

  $O(\log n)$
• What characterizes an efficient algorithm?

  Completes tasks quickly with minimal resources